I am new to appimage and linux as a whole. I am wondering if i create appimage of applications that save data in the home folder, like firefox and thunderbird, will they still save their profiles in the home folder?

AppImages are immutable, which means read-only, by design. Applications should write to $HOME. This is the same when you install an application using the package manager to /usr. Then the application, running as a normal user, will also not be able to write there.

What do you mean read-only by design? I downloaded chromium and the .appimage file had write permissions for owner and group. Do i have to remove them? Also, if i want to edit some file inside the bundle how can i do that?

What is inside an AppImage cannot be changed without unpacking and re-packing the filesystem contained inside the AppImage, because ISO9660 (type 1 AppImages) or squashfs (type 2 AppImages) is used, which are by nature read-only.

I am new to appimage and linux as a whole. I am wondering if i create appimage of applications that save data in the home folder, like firefox and thunderbird, will they still save their profiles in the home folder?

An user in our chat has recently made a Firefox AppImage that does that, by exporting $HOME from a custom AppRun bash script.